Problem: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 6x + 9$ and $ BC = 3x + 36$ Find $AC$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {6x + 9} = {3x + 36}$ Solve for $x$ $ 3x = 27$ $ x = 9$ Substitute $9$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 6({9}) + 9$ $ BC = 3({9}) + 36$ $ AB = 54 + 9$ $ BC = 27 + 36$ $ AB = 63$ $ BC = 63$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {63} + {63}$ $ AC = 126$